A Magnetic Attraction
TEACHER NOTES
SCIENCE NSPIRED
Science Objectives

Students will map and describe the magnetic field around a
permanent magnet or electromagnet.

Students will determine the direction and strength of the force a
magnet exerts on a current-carrying wire or loop.
Vocabulary

magnetic field

magnetic permeability constant
TI-Nspire™ Technology Skills:

magnetic moment
 Download a TI-Nspire
document
About the Lesson
 Open a document

In this activity, students will investigate the relationship between
 Move between pages
magnetic field strength and distance.
 Collect data with Sensors

As a result, students will:

Develop a mathematical model of magnetic field strength.
Tech Tips:

Use the model to calculate the magnetic moment of the field.
Access free tutorials at
http://education.ti.com/calculator
s/pd/US/Online-
TI-Nspire™ Navigator™
Learning/Tutorials

Send out the A_Magnetic_Attraction.tns file.

Monitor student progress using Screen Capture.

Use Live Presenter to spotlight student answers.
Activity Materials

A_Magnetic_Attraction.tns document

TI-Nspire™ Technology

magnet

meterstick

Vernier Magnetic Field Sensor

Vernier EasyLink™or Go!®Link interface

pen or pencil

blank sheet of paper

tape
©2013 Texas Instruments Incorporated
Lesson Files:
Student Activity
 A_Magnetic_Attraction
_Student.doc
 A_Magnetic_Attraction
_Student.pdf
TI-Nspire document
 A_Magnetic_Attraction.tns
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A Magnetic Attraction
TEACHER NOTES
SCIENCE NSPIRED
Discussion Points and Possible Answers
Students will probably be familiar with the effects of magnets, but may not know the quantitative
relationships between magnetic field strength and distance. Before beginning this activity, review the
concepts of magnetic field strength, magnetic moment, and magnetic permeability with students.
You should experiment with the magnets students will be using to determine which units (gauss or
millitesla) students should use. In general, unless students are using a very strong magnet, gauss is the
most appropriate unit. You should also experiment with appropriate distances for students to use.
Move to page 1.2.
1. Students should read the first page. They will then place a meterstick on a flat, level surface. They
should place the Vernier Magnetic Field Sensor at the zero end of the meterstick. Tell students to
orient the sensor so the white dot is pointing along the axis of the meterstick. They should tape the
sensor in place so that it does not move during the experiment.
Move to page 1.3.
2. Page 1.3 is a blank DataQuest application. Students should
connect the Vernier Magnetic Field Sensor to an EasyLink
interface (if using a handheld) or a Go!Link interface (if using a
computer). They then will connect the EasyLink or Go!Link to
their handheld or computer.
3. Tell students to use mT units for this lab. Students can change
the units from the Sensors menu (Menu > Experiment > Set Up
Sensors > Change Units > Magnetic Field).
4. Students should make sure there are no magnets near the sensor and then zero the sensor.
(Menu > Experiment > Set Up Sensors > Zero).
5. Next, students set up the data collection software to Events with Entry mode (Menu > Experiment
> Collection Mode). Students change the name of the event to “Distance” and units to “cm.”
6. Tell students where to place the Magnetic Field Sensor for the initial measurement. They should
keep the same orientation between the magnet and the sensor for all measurements. The magnet
should have its South pole facing the white dot of the sensor, with the magnet’s axis (the line
connecting the North and South poles) parallel to the meterstick. Readings will be collected every 1
cm starting from the starting point. For the sample data shown at the right, readings were collected
every 1 cm starting at the 5 cm mark. Students press Start Collection
and then will click on the Keep Button
to start collecting data,
to keep the data collected.
7. Students move the magnet to the next mark and repeat the data collection, taking care to maintain
the same orientation between the magnet and the sensor.
8. Students repeat the data collection eight more times. Once they have collected ten data points, they
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A Magnetic Attraction
TEACHER NOTES
SCIENCE NSPIRED
can click on Stop Data Collection
and disconnect the sensor.
Move to page 1.4
9. Page 1.4 contains a blank Lists & Spreadsheet application.
Students set Column A to display the distance data they collected
(press h > Link To: select the variable from the list). They set
Column B to the magnetic field strength data they collected.
Move to page 1.5
10. Page 1.5 contains a blank Graphs & Geometry application. Students press Menu > Graph Type >
Scatter Plot, then h > Link To: to select the distance variable for x. They repeat this to select the
magnetic field strength variable for y, and then press
·. To adjust the scale for the graph, they
may need to press Menu > Window/Zoom > Zoom – Data.
Return to page 1.4
11. Students highlight Columns A and B. They press Menu >
Statistics > Stat Calculations > Power Regression. This
function tells the handheld to calculate an equation of the form y =
b
ax that best fits the highlighted data. Students select OK to carry
out the regression.
Move to page 1.5.
12. Students change the plot type to Function (Menu > Graph Type > Function). They select f1(x)
from the function list at the bottom of the screen and press
· to plot the regression equation on
the graph. Students record this equation on a separate sheet of paper.
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A Magnetic Attraction
TEACHER NOTES
SCIENCE NSPIRED
Part 2: Building a Model for the Relationship
Move to page 1.5
1. On page 1.5, students hide the graph of f1(x) using the Show/Hide tool (Menu > Actions >
Hide/Show). They click on the graph to hide it and then use the Trace tool (Menu > Trace > Graph
Trace) to determine and mark the coordinates of the leftmost point. As established in Part 1,
magnetic field strength and distance are related by an inverse-cube law. That is, the equation relating
k
field strength (I) and distance (d) takes the form B 
, where k is a constant. Students use
d3
substitution to find the value of k that makes the equation above true for the leftmost point on the
graph. They record the value of k on a separate sheet of paper.
2. Students place a text box (Menu > Actions > Text) somewhere on the page. They type the value of
·. Then, they click once on the value (it should
be highlighted in gray) and press h. They select Store Var, type k, and press ·. This will
k that they calculated into this text box and press
assign the number in the text box to the variable k.
3. In the f2(x) line of the function bar on page 1.5, Students type k/x and press ·. (They may need
3
to change the graph type to Function in order to see the function bar.) A graph of the estimated
equation relating magnetic field strength to distance should appear on the screen.
4. Students can vary the value of k (by editing the text box) to produce a better fit to the data. They
record the best-fit value of k on a separate sheet of paper.
Part 3: Determining the Magnetic Moment
The equation relating magnetic field strength (B) to distance (d) is given below ( 
permeability constant, and  is the magnetic moment of the field).
B 
0
is the magnetic
0
2
g
4
d3
In Part 2, students approximated this equation with the function B 
k
d3
, and then calculated the value
of k for their data. They will now use this value of k to calculate the magnetic moment of the field using
20
 k
the equation : 4
.
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A Magnetic Attraction
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SCIENCE NSPIRED
Move to page 1.6.
5. This page contains a Calculator application. The magnetic
permeability constant, 0 , is equal to 4  104 . Define the
variable mu0 as 4  104 as shown. You should make sure to
use the := notation when you define the value of the constant.
6. Next, students use the nSolve function to solve the equation
above for  , entering the expression as shown at the right. They
then record the calculated value of  on a separate sheet of
paper. (In this equation, 0 and  are constants.)
Have students answer questions on the activity sheet.
Q1.
How well do the results of the power regression support the “ideal” relationship between field
strength and distance: B 
0
4
g
2
d3
? Explain your answer.
Answer: The results of the power regression agree with the “ideal” relationship. The ideal
relationship indicates that magnetic field intensity should decrease in inverse proportion to
distance cubed, and the power regression yields an exponent of nearly –3.
Q2.
What is the value of k that you calculated from the data?
Answer: Students’ values of k will vary.
Q3.
What is the value of  that you calculated from the data?
Answer: Students’ values of  will vary.
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A Magnetic Attraction
TEACHER NOTES
SCIENCE NSPIRED
Q4.
Electric currents produce magnetic fields. For a single loop of wire, the magnetic moment of the
field is   IA , where  is the magnetic moment, I is the current, and A is the area of the loop
through which the current flows.
Suppose the magnetic field in this activity were produced by a round magnet with a radius of
29 mm. What current would be required to produce an equivalent magnetic field in a loop of wire
2
with the same radius as the magnet? (Note: The units of  that you calculated are m • A.)
Answer: If the radius of the wire loop is 29 mm (0.029 m) and the magnetic moment of the field is
2
0.4995 m • A, the current in the loop can be calculated as follows:
  IA  I( r 2)
0.4995 m2gA  (I)()(0.029 m)2
I 
0.4995
 189 A
0.00264
TI-Nspire Navigator Opportunities
Use the Ti-Nspire Navigator System to collect, grade, and save the .tns file to the
Portfolio. Use Slide Show to view student responses.
Wrap Up
The students should collect data on the .tns file. When students are finished with the
activity, pull back the .tns file using TI-Nspire Navigator. Discuss activity questions using
Slide Show.
Assessment

Formative assessment will consist of questions in the activity sheet.

Summative assessment will consist of questions/problems on the chapter test.
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